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Common Core: High School - Number and Quantity : High School: Number and Quantity

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

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All Common Core: High School - Number and Quantity Resources

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If $\left \| v\right \|=34$ , and $\left \| w\right \|=17$ , and the angle in between them is $10^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=13.56$

$\left \| v+w\right \|=17.51$

$\left \| v+w\right \|=18.09$

$\left \| v+w\right \|=14.69$

$\left \| v+w\right \|=17.84$

Correct answer:

$\left \| v+w\right \|=17.51$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=17 , b=10 , and $C=10^{\circ}$ , then

$c^2=17^2+34^2-2\cdot34\cdot17\cos(10^{\circ})$

$c^2=289+1156-34\cdot34\cos(10^{\circ})$

$c^2=1445-1156\cos(10^{\circ})$

c^2=1445-1138.438

c^2=306.562

$\sqrt{c^2}=\sqrt{306.562}$

$c=\sqrt{306.562}\approx17.51$

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Example Question #2 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If $\left \| v\right \|=18$ , and $\left \| w\right \|=19$ , and the angle in between them is $131^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=33.67$

$\left \| v+w\right \|=32.89$

$\left \| v+w\right \|=34.90$

$\left \| v+w\right \|=37.92$

$\left \| v+w\right \|=31.56$

Correct answer:

$\left \| v+w\right \|=33.67$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=18 , b=2 , and $C=106^{\circ}$ , then

$c^2=18^2+19^2-2\cdot18\cdot19\cos(131^{\circ})$

$c^2=324+361-36\cdot19\cos(131^{\circ})$

$c^2=685-684\cos(131^{\circ})$

$c^2=685-684\cdot-0.656059$

c^2=685+448.7444

c^2=1133.744

$\sqrt{c^2}=\sqrt{1133.744}$

$c=\sqrt{1133.744}\approx33.67$

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Example Question #1 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If $\left \| v\right \|=4$ , and $\left \| w\right \|=23$ , and the angle in between them is $149^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=28.13$

$\left \| v+w\right \|=27.76$

$\left \| v+w\right \|=27.23$

$\left \| v+w\right \|=24.57$

$\left \| v+w\right \|=26.42$

Correct answer:

$\left \| v+w\right \|=27.23$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=4 , b=23 , and $C=149^{\circ}$ , then

$c^2=4^2+23^2-2\cdot4\cdot23\cos(149^{\circ})$

$c^2=16+529-8\cdot23\cos(149^{\circ})$

$c^2=545-184\cos(149^{\circ})$

$c^2=545-184\cdot-0.8571673$

c^2=584+157.7188

c^2=741.7188

$\sqrt{c^2}=\sqrt{741.7188}$

$c=\sqrt{741.7188}\approx27.23$

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Example Question #4 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If $\left \| v\right \|=14$ , and $\left \| w\right \|=1$ , and the angle in between them is $76^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=14.09$

$\left \| v+w\right \|=13.79$

$\left \| v+w\right \|=17.94$

$\left \| v+w\right \|=14.25$

$\left \| v+w\right \|=13.62$

Correct answer:

$\left \| v+w\right \|=13.79$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=14 , b=1 , and $C=76^{\circ}$ , then

$c^2=14^2+1^2-2\cdot14\cdot1\cos(76^{\circ})$

$c^2=196+1-28\cdot1\cos(76^{\circ})$

$c^2=197-28\cos(76^{\circ})$

$c^2=197-28\cdot0.2419219$

c^2=197-6.773813

c^2=190.2262

$\sqrt{c^2}=\sqrt{190.2262}$

$c=\sqrt{190.2262}\approx13.79$

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Example Question #11 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If $\left \| v\right \|=9$ , and $\left \| w\right \|=28$ , and the angle in between them is $150^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=36.89$

$\left \| v+w\right \|=35.76$

$\left \| v+w\right \|=36.08$

$\left \| v+w\right \|=33.98$

$\left \| v+w\right \|=29.53$

Correct answer:

$\left \| v+w\right \|=36.08$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=9 , b=28 , and $C=150^{\circ}$ , then

$c^2=9^2+28^2-2\cdot9\cdot28\cos(150^{\circ})$

$c^2=81+784-18\cdot28\cos(150^{\circ})$

$c^2=865-504\cos(150^{\circ})$

$c^2=865-504\cdot-0.8660254$

c^2=865+436.4768

c^2=1301.477

$\sqrt{c^2}=\sqrt{1301.477}$

$c=\sqrt{1301.477}\approx36.08$

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Example Question #12 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If $\left \| v\right \|=12$ , and $\left \| w\right \|=34$ , and the angle in between them is $54^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=26.67$

$\left \| v+w\right \|=28.14$

$\left \| v+w\right \|=24.87$

$\left \| v+w\right \|=28.64$

$\left \| v+w\right \|=29.67$

Correct answer:

$\left \| v+w\right \|=28.64$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=12 , b=34 , and $C=54^{\circ}$ , then

$c^2=12^2+34^2-2\cdot12\cdot34\cos(54^{\circ})$

$c^2=144+1156-24\cdot34\cos(54^{\circ})$

$c^2=1300-816\cos(54^{\circ})$

$c^2=1300-816\cdot0.5877853$

c^2=1300-479.6328

c^2=820.3672

$\sqrt{c^2}=\sqrt{820.3672}$

$c=\sqrt{820.3672}\approx28.64$

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Example Question #1 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<-3,4> , and w=<2,3> , what is v-w ?

Possible Answers:

v-w=<1,-5>

v-w=<-5,1>

v-w=<-5,-1>

v-w=<5,-1>

v-w=<5,1>

Correct answer:

v-w=<-5,1>

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=-3$

$(x\:\mbox{component in}\: w)=2$

$(y\: \mbox{component in}\: v)=4$

$(y\: \mbox{component in}\: w)=3$

x=-3-2=-5

y=4-3=1

So our final answer is <-5,1> .

Below is a visual representation.

Vecsub

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Example Question #2 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<4,-2> , and w=<4,3> , what is v-w ?

Possible Answers:

v-w=<0,5>

v-w=<0,-5>

v-w=<8,1>

v-w=<5,0>

v-w=<-5,0>

Correct answer:

v-w=<0,-5>

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=4$

$(x\:\mbox{component in}\: w)=4$

$(y\: \mbox{component in}\: v)=-2$

$(y\: \mbox{component in}\: w)=3$

x=4-4=0

y=-2-3=-5

So our final answer is <0,-5> .

Below is a visual representation.

Screen shot 2016 03 08 at 9.31.39 am

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Example Question #3 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<-10,5> , and w=<-6,-7> , what is v-w ?

Possible Answers:

v-w=<-16,2>

v-w=<12,4>

v-w=<-4,12>

v-w=<12,-4>

v-w=<4,12>

Correct answer:

v-w=<-4,12>

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=-10$

$(x\:\mbox{component in}\: w)=-6$

$(y\: \mbox{component in}\: v)=5$

$(y\: \mbox{component in}\: w)=-7$

x=-10-(-6)=-10+6=-4

y=5-(-7)=5+7=12

So our final answer is <-4,12> .

Below is a visual representation.

Screen shot 2016 03 08 at 9.52.05 am

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Example Question #1 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<1,1> , and w=<-7,-9> , what is v-w ?

Possible Answers:

v-w=<-10,-8>

v-w=<8,-10>

v-w=<-8,10>

v-w=<8,10>

v-w=<10,8>

Correct answer:

v-w=<8,10>

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=1$

$(x\:\mbox{component in}\: w)=-7$

$(y\: \mbox{component in}\: v)=1$

$(y\: \mbox{component in}\: w)=-9$

x=1-(-7)=1+7=8

y=1-(-9)=1+9=10

So our final answer is <8,10> .

Below is a visual representation.

Screen shot 2016 03 08 at 10.22.33 am

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All Common Core: High School - Number and Quantity Resources

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Common Core: High School - Number and Quantity : High School: Number and Quantity

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

All Common Core: High School - Number and Quantity Resources

Example Questions

Example Question #1 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

Example Question #2 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

Example Question #1 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

Example Question #4 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

Example Question #11 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

Example Question #12 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

Example Question #1 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #2 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #3 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #1 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

All Common Core: High School - Number and Quantity Resources

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