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2 years ago

7

Which of the following shows the numbers in the box below listed in increasing order?

1 answer:

Anarel [89]2 years ago

5 0

9514 1404 393

Answer:

(A) -2, 3/7, 1/2, 1.2

Step-by-step explanation:

The numbers are in increasing order when they are listed left-to-right as they appear on the number line.

The only numbers that may give you trouble are 3/7 = 6/14 and 1/2 = 7/14.

The negative number is less than any positive number. 1.2 is greater than any fraction that is less than 1.

The correct ordering is found in choice A.

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H(-6) = 2(-6) + 5
h(-6) = -12 + 5
Solution: h(-6) = -7

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2 years ago

Read 2 more answers

The Colonel spots a campfire at a bearing N 59∘59∘ E from his current position. Sarge, who is positioned 242 feet due east of th

Rashid [163]

Answer:

i. Colonel is about 201 feet away from the fire.

ii. Sarge is about 125 feet away from the fire.

Step-by-step explanation:

Let the Colonel's location be represented by A, the Sarge's by B and that of campfire by C.

The total angle at the campfire from both the Colonel and Sarge = $59^{0}$ + $34^{0}$

= $93^{0}$

Thus,

<CAB = $90^{0}$ - $59^{0}$ = $31^{0}$

<CBA = $90^{0}$ - $34^{0}$ = $56^{0}$

Sine rule states;

$\frac{a}{Sin A}$ = $\frac{b}{Sin B}$ = $\frac{c}{Sin C}$

i. Colonel's distance from the campfire (b), can be determined by applying the sine rule;

$\frac{b}{Sin B}$ = $\frac{c}{Sin C}$

$\frac{b}{Sin 56^{0} }$ = $\frac{242}{Sin 93^{0} }$

$\frac{b}{0.8290}$ = $\frac{242}{0.9986}$

cross multiply,

b = $\frac{0.8290*242}{0.9986}$

= 200.8993

Colonel is about 201 feet away from the fire.

ii. Sarge's distance from the campfire (a), can be determined by applying the sine rule;

$\frac{a}{Sin A}$ = $\frac{c}{Sin C}$

$\frac{a}{Sin 31^{0} }$ = $\frac{242}{Sin 93^{0} }$

$\frac{a}{0.5150}$ = $\frac{242}{0.9986}$

cross multiply,

a = $\frac{0.5150*242}{0.9986}$

= 124.8073

Sarge is about 125 feet away from the fire.

8 0

2 years ago

A camera is mounted at a point 4000 feet away from a geyser. If the water is rising vertically at 900 ft/s when it is 3000 feet

Leno4ka [110]

Answer:

$\dot \theta = 0.144\,\frac{rad}{s}$ , $\dot \theta = 8.251\,\frac{deg}{s}$ (Option B)

Step-by-step explanation:

The trigonometric diagram is included herein as attachment. The expression is presented below:

$\tan \theta = \frac{y}{x}$

Where:

$x$ - Horizontal distance between the geyser and the camera.

$y$ - Vertical distance between the geyser and the camera.

The rate of change in terms of time is:

$\dot \theta \cdot \sec^{2}\theta = \frac{\dot y\cdot x-y\cdot \dot x}{x^{2}}$

$\dot \theta \cdot \left(\frac{1}{\cos^{2}\theta} \right) = \frac{\dot y \cdot x - y\cdot \dot x}{x^{2}}$

$\dot \theta = \left(\frac{\dot y \cdot x - y \cdot \dot x}{x^{2}} \right)\cdot \cos^{2}\theta$

$\dot \theta = \left(\frac{\dot y \cdot x - y\cdot \dot x}{x^{2}} \right)\cdot \left(\frac{x^{2}}{x^{2}+y^{2}} \right)$

$\dot \theta = \frac{\dot y \cdot x - y\cdot \dot x}{x^{2}+y^{2}}$

Finally,

$\dot \theta = \frac{\left(900\,\frac{ft}{s} \right)\cdot (4000\,ft)-(3000\,ft)\cdot \left(0\,\frac{ft}{s} \right)}{(4000\,ft)^{2}+(3000\,ft)^{2}}$

$\dot \theta = 0.144\,\frac{rad}{s}$

$\dot \theta = 8.251\,\frac{deg}{s}$

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2 years ago