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4 years ago

How would I work this out

Mathematics

1 answer:

liraira [26]4 years ago

5 0

Answer:

10.1

Step-by-step explanation:

You can find the length of XY by first finding YZ using the Pythagorean theorem. Then subtract the length from 15 for the length of the other triangle. Use the Pythagorean theorem again to find XY.

The Pythagorean theorem is used for all right triangles and is the formula $a^2 + b^2 = c^2$ . Here a = 4, b is unknown and c = 7.

So $4^2 + b^2 = 7^2\\16 + b^2 = 49\\b^2 = 33\\b = \sqrt{33} =5.75$

Subtract 5.75 from 15.

15 - 5.75 = 9.25.

Repeat the Pythagorean Theorem again with a = 4, b = 9.25 and c is unknown. Solve for c. This is XY.

$4^2 + 9.25^2 = c^2\\16 + 85.56 = c^2\\101.6 = c^2\\10.1 = c$

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Step-by-step explanation:

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3 years ago

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3 years ago

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Find g(x), where g(x) is the reflection across the x-axis of f(x)= – 4(x–10)2+3.

Dahasolnce [82]

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3 years ago

Find the surface area of the figure.

guajiro [1.7K]

Given:

Given that the radius of the cylinder is 6 m.

The height of the cylinder is 7 m.

We need to determine the surface area of the cylinder.

Surface area of the cylinder:

The surface area of the cylinder can be determined using the formula,

$SA=2 \pi r(r+h)$

where r is the radius and h is the height of the cylinder.

Substituting r = 6 and h = 7 in the above formula, we get;

$SA=2 (3.14)(6)(6+7)$

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4 0

4 years ago

Amir throws a stone off of a bridge into a river. The stone's height (in meters above the water) ttt seconds after Amir throws i

Harrizon [31]

Answer:

1) The vertex form of $h(t) = -5\cdot t^{2}+20\cdot t +160$ is $h -180 = -5\cdot (t-2)^{2}$ , 2) The stone reaches its maximum height 2 seconds after being thrown.

Step-by-step explanation:

1) Given that height of the stone is represented by a second-order polynomial, which depicts a parabola as graph. The best approach to determine the instant when stone reaches its highest is by vertex form, whose form is:

$h-k = C\cdot (t-r)^{2}$

Where:

$r$ , $k$ - Instant and maximum height of the stone, measured in seconds and meters.

$C$ - Vertex constant, which must be negative as there is an absolute maximum, measured in meters per square second.

Let be $h(t) = -5\cdot t^{2}+20\cdot t +160$ , which is transformed into vertex form:

i) $h = -5\cdot t^{2}+20\cdot t +160$ Given

ii) $h = -5\cdot (t^{2}-4\cdot t -32)$ Distributive property/ $(-a)\cdot b = -a\cdot b$

iii) $h = -5\cdot [(t^{2}-4\cdot t +4)+(-36)]$ Existence of additive inverse/Definitions of addition and subtraction

iv) $h = (-5)\cdot (t-2)^{2}+180$ Distributive property/ $(-a)\cdot (-b) = a\cdot b$ /Perfect square binomial

v) $h -180 = -5\cdot (t-2)^{2}$ Compatibility with addition/Existence of additive inverse/Modulative property/Definition of subtraction/Result

The vertex form of $h(t) = -5\cdot t^{2}+20\cdot t +160$ is $h -180 = -5\cdot (t-2)^{2}$ .

2) The time can be extracted from previous results, which indicates that stone reaches its maximum height 2 seconds after being thrown.

4 0

3 years ago